MAT Exam 2020 Paper

Concept:The total capacity of the tank is taken as $V$, and the changing fuel levels are expressed as fractions of $V$ to form a linear equation.Explanation:Let the total capacity of the fuel tank be $V$ litres.Initially, the fuel in the tank is $\frac{1}{5}$ of the full tank, i.e., $\frac{V}{5}$ litres.After adding 22 more litres, the fuel becomes $\frac{3}{4}$ of the full tank, i.e., $\frac{3V}{4}$ litres.So, the equation is:$$\frac{V}{5} + 22 = \frac{3V}{4}$$Rearranging the terms:$$\frac{3V}{4} - \frac{V}{5} = 22$$Taking LCM of 4 and 5 as 20:$$\frac{15V - 4V}{20} = 22$$$$\frac{11V}{20} = 22$$Multiplying both sides by 20:$$11V = 440$$$$V = \frac{440}{11} = 40$$Answer:The capacity of the fuel tank is 40 litres, which is Option A.